In this paper by me Church's thesis meets quantum mechanics paper #49 here http://rangevoting.org/WarrenSmithPages/homepage/works.html it was proven that solving the quantum N-body problem is "efficiently simulable" in a certain sense. This sense is, with probability 99.99999999%, easier than NP-complete, i.e. my paper "proves" this is NOT and cannot be, NP-hard. The reason proves is in quotes is that this is only true if certain well known conjectures about NP are true (e.g. P not equal NP).